I have just learnt that a colleague of mine does sudoku. He tells me that the hints (which he occasionally looks at) seem to rely on entering candidate numbers in each cell - he said that he finds this confusing. I retorted that for "difficult" puzzles I thought that everyone did this (HAD to do this, in fact). He said that he never did this - he just reasons out every cell, only very rarely making any sort of margin notes. I was somewhat dumbfounded - how can he hold all the information in his head? Maybe they are easier puzzles I wondered? They are categorised from easy to diabolical and appear in the UK Daily Telegraph - must admit that I haven't looked at them.
Can anyone shed any comment on this? Having long ago resorted to at least some pencilling in of candidates for anything beyond medium (from this site, the only sudokus that I regularly try) it made me feel rather inadequate!!

There is a "super champion" that claims (on some Internet page) that he is solving in about a couple of minutes (up to 5-7) every Sudoku without any need of writting something down.
Did not see him life, so I am passing you the info, just to feel better.

This champion should still keep in mind:
"there is always someone better than me"
(even an old stupid 286 PC can beat him solving in matter of seconds, for what he needs a couple of minutes).

I have looked at some of the "Daily Telegraph" puzzles -- they're composed by Michael Mepham, and you can find some of them on-line (http://www.sudoku.org.uk/backpuzzles.htm). Just for grins I just now worked a "moderate" puzzle from that site -- it was comparable to a "medium" puzzle from the Daily Sudoku, in my estimation.

When I first started working these puzzles (last April, as I recall) I made a lot of marks on the paper. I didn't even have a very good system for making those marks. After a while I developed a system that works for me -- I avoid making any marks (except single values, once I've reasoned one or two of those out) as long as I possibly can. Then, if I have to, I start marking the "candidate lists" of length 2. I try not to mark candidate lists of length 3 or longer -- those usually just get me confused.

The longer I've been at this, the fewer marks I've had to make. I'm pretty sure this is partly from familiarity with the kinds of clues Samgj commonly builds into his puzzles, and partly from practice -- I can visualize hidden pairs now, for instance. Six months ago I had a hard time spotting them, and I always wrote them down.

Lately I've been trying to work all of the Daily Sudoku puzzles (the 9x9 versions) without making any "pencil marks." I can't always get through the "very hard" puzzles this way, and sometimes a "hard" puzzle trips me up. But I can almost always get through the "medium" and "easy" puzzles without marking any candidates.

I don't think you should feel "inadequate" -- each of us has unique talents. Try looking at the puzzle as a way to enhance and improve your powers of concentration -- you'll get better as you get more practice! dcb

I try not to mark candidate lists of length 3 or longer -- those usually just get me confused.

I am a specialist stickler in this respect: I forbid myself 3 or longer.
But this is to avoid the tedium; such candidate lists are just too viscous.

However:
Full candidate lists provide a canvas for 'narrowing down'.
You need some way of noting (non-trivial) exclusions to compensate for the loss of this canvas. I mean the sort of thing you see in someone_somewhere's tracings.

I am a specialist stickler in this respect: I forbid myself 3 or longer. But this is to avoid the tedium; such candidate lists are just too viscous.

That's an interesting definition for "viscous." I agree that updating long lists of candidates is a lot of work. But another thing I've noticed is that many times, when there are a large number of unresolved cells and I've written down some candidate pairs, I can easily visualize the longer candidate lists simply by adding up the pairs I've already detected (possibly in conjunction with one or two inclusions and/or exclusions).

For instance, if there are five empty cells in a row and I've already noticed a pair {3, 4} in one of those, and another pair {5, 7} in a second spot, I can be sure that the other three cells in that row contain some combination of {3, 4, 5, 7} plus one other value. And often enough that one other value ends up being a "hidden single." dcb